The following solves the first 3 eigenvalues of the following simple 3D-Schrödinger equation, but I do not know how to use the interpolating eigenfunctions, i.e.,
funs[[2]][0,0,0]
does not return a value. This does not happen in 2-Dimensions. What am I doing wrong?
Clear["Global`*"]
Rcube = ImplicitRegion[Abs[x] <= 1 && Abs[y] <= 1 && Abs[z] <= 1, {x, y, z}];
F[x_, y_, z_] := If[x + y + z <= -2, 0, 1];
{vals, funs} = NDEigensystem[{-Laplacian[u[x, y, z], {x, y, z}] + F[x, y, z]*u[x, y, z],
DirichletCondition[u[x, y, z] == 0, True]}, u[x, y, z],
Element[{x, y, z}, Rcube], 3]
NDEigensystem[]
to return objects of the formifun[x, y, z]
instead ofifun
, whereifun
is anInterpolatingFunction[]
. Try{vals, funs} = NDEigensystem[{-Laplacian[u[x, y, z], {x, y, z}] + Boole[x + y + z > -2] u[x, y, z], DirichletCondition[u[x, y, z] == 0, True]}, u, {x, y, z} ∈ Rcube, 3]
and thenfuns[[2]][0, 0, 0]
. (Note the second argument I gave!) $\endgroup$